if x is squared, that will be biggest by the end because it gets bigger the quickest. x^2 + 4 is always 4 greater than x^2, no matter what the value of x is.
5x+3 is always 3 greater than 5x also.
Besides that, you can rank them based on their slopes (5x < 7x < 8x, etc.)
So,
5x
5x + 3
7x
8x + 3
x^2
x^2 + 4
You can also just say “eventually” means that they’re asking to find the values of each when x is really big. so just choose x=100, and plug that into each one.
So, to check that order:
5(100) = 500
5(100) + 3 = 503
7(100) = 700
8(100) + 3 = 803
(100)^2 = 10,000
(100)^2 + 4 = 10,004
Those are in ascending order, so that must be the right order!
